Free floating, bedding, trigger improvements and frequently re-crowning the muzzle all have a positive affect on .22 rimfire accuracy. As does correctly setting the headspace in the bolt, having the rifling begin to engrave the bullet upon chamberiing and proper shape of the firing pin and adequate strength of the firing pin spring. Finding the rimfire ammo your rifle likes is also a very good idea. You may be lucky & find lower priced ammo that your rifle likes. BUT remember that with increasing price, comes increasing consistency, that is, fewer fliers.
Remember, that with the low velocity of .22 RF, your follow through, consistent positioning, and consistent hold are very important.

A great deal depends on what rifle you have. It a heavy barreled target rifle with match grade sights?
However, free floating guarantees nothing on any rifle. Some rifles like it. Some do not. The only way to find out if yours does is to try it. Isn't a big deal to put a pressure point back in. Mind you, like g.willikers says, if you haven't tried a box of as many brands of ammo as you can to find the ammo your rifle shoots best, you need to do that first. The price of that ammo means nothing either.
Having to frequently re-crowning the muzzle means you're abusing the rifle.

One change at a time, and extensive notebook, and practice practice practice!

__________________1. The pattern board is your friend, use the Dam thing!!!2. The maximum range of a firearm and/or cartridge, is usually measured in miles, and means nothing.2a. The effective range of a firearm and/or cartridge, is usually (the ability of the shooter) measured in yards, and means everything.

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